PLEASE ANSWER THE SECTION SUMMARIZE YOUR ANALYSIS IN YOUR REPORT AND COMPLETE TH
ID: 1111645 • Letter: P
Question
PLEASE ANSWER THE SECTION SUMMARIZE YOUR ANALYSIS IN YOUR REPORT AND COMPLETE THE TABLE 2 SECTIONS D AND E
The ABC Mining Company uses capital (mining equipment) and labor (workers) to mine copper ore. Various sizes of ore-mining equipment, as measured by its brake horsepower (bhp) rating, are available to the company. The amount of ore mined during a given period (Q) is a function only of the number of workers assigned to the crew (L) operating a given type of equipment (K). The data in the table below show the amount of ore produced (measured in tons) when various sizes of crews are used to operate the equipment.
Units of capital employed, bhp (K)
Output quantity, tons (Q)
2000
0
13
44
50
55
60
62
64
65
66
67
1750
0
16
44
55
60
62
63
64
65
66
66
1500
0
16
29
55
60
62
63
64
65
65
65
1250
0
16
29
55
58
61
63
64
64
64
64
1000
0
10
24
44
55
60
62
63
63
63
62
750
0
6
16
29
44
55
60
62
62
61
59
500
0
3
6
16
29
43
55
58
60
59
56
250
0
1
2
4
6
16
29
44
50
55
52
Units of labor employed, workers (L)
0
1
2
3
4
5
6
7
8
9
10
PREPARATORY WORK (EXCEL):
(P1) PRODUCTION FUNCTION WITH ONE VARIABLE INPUT
Suppose, that the amount of capital input K (the size of mining equipment) employed in the production process is a fixed factor. Specifically, suppose that the firm owns or leases a piece of mining equipment having a 750-bhp rating. Depending on the amount of labor input L used to operate the 750-bhp equipment, varying quantities of output will be obtained, as shown in the 750 row of the table above.
(P1.1) Complete Columns (c) and (d) in Table 1 in the attached Excel file, that is, calculate the Marginal Product of Labor (MPL) and the Average Product of Labor (APL).
(P1.2) In one graph, plot the (i) total product, (ii) marginal product, and (iii) average product functions.
(P1.3) Determine the boundaries of the three stages of production.
(P2) DETERMINING THE OPTIMAL USE OF THE VARIABLE INPUT
With one of the inputs (K) fixed in the short run, determine the optimal quantity of the variable input (L) to employ in the production process. Suppose that the ore-mining company can employ as much labor (L) as it needs by paying the workers $50 per shift. Suppose further that the firm can sell all the ore it can produce at a price of $10 per ton. In other words, both the input (i.e., labor) market and the product market are assumed to be perfectly competitive.
(P2.1) Complete Columns (e) - (j) in Table 1 in the attached Excel file, that is, calculate the Total and Marginal Revenue Products (TRP and MRP) and the Total and Marginal Labor Costs (TLC and MLC).
(P2.2) Determine the optimal labor input when K=750 bhp.
(P3) PRODUCTION WITH MULTIPLE VARIABLE INPUTS
Suppose now that both capital (measured by the maximum bhp rating of the equipment) and labor (measured by the number of workers) are variable inputs to the ore-mining process. The firm can choose to operate the production process using any of the capital-labor combinations shown previously in Table 0.
(P3.1) In Table 0, identify the isoquant for Q = 29 tons. Compete Columns (b) and (c) in Table 2 in the attached Excel file.
(P3.2) Compete Column (d) in Table 2 in the attached Excel file, that is, compute the Marginal Rate of Technical Substitution (MRTS) along the isoquant for Q = 29 tons.
(P4) DETERMINING THE OPTIMAL USE OF MULTIPLE VARIABLE INPUTS
As we assumed before, suppose that the cost per worker is $50 per period. Suppose further that mining equipment can be leased at a price of $0.20 per bhp per period.
(P4.1) Compete Column (e) in Table 2 in the attached Excel file, that is, compute the Total Cost for different combinations of labor and capital for the isoquant Q = 29 tons.
(P4.2) In one graph, plot the isoquant curve for Q = 29 tons and the isocost line tangent to the isoquant. Show capital input (K) on the vertical axis and labor input (L) on the horizontal axis. HINT: To construct this graph in Excel, you may need to know how to plot continuous lines when the data range contains blank cells in Excel. The instructions are provided in the file available within the "Lab assignment # 4" folder.
(P4.3) Determine the optimal combination of labor and capital inputs when Q = 29 tons.
SUMMARIZE YOUR ANALYSIS IN YOUR REPORT (PDF):
(a) Comment on the following questions (in your explanations refer to Appendix 1 or Appendix 2):
(a1) Describe the boundaries of the three stages of production. Explain fully.
(a2) Describe the optimal labor input when K=750 bhp. Explain fully.
(a3) Comment on the magnitude of MRTS as we move along the isoquant you identified in P3. Explain fully.
(a4) Describe the optimal combination of labor and capital inputs when Q = 29 tons. Explain fully.
(b) Attach the graph you created in P1.2 as Appendix 1.
(c) Attach the graph you created in P4.2 as Appendix 2.
Use the following data, please use tables provided for answers, thanks:
Units of capital employed, bhp (K)
Output quantity, tons (Q)
2000
0
13
44
50
55
60
62
64
65
66
67
1750
0
16
44
55
60
62
63
64
65
66
66
1500
0
16
29
55
60
62
63
64
65
65
65
1250
0
16
29
55
58
61
63
64
64
64
64
1000
0
10
24
44
55
60
62
63
63
63
62
750
0
6
16
29
44
55
60
62
62
61
59
500
0
3
6
16
29
43
55
58
60
59
56
250
0
1
2
4
6
16
29
44
50
55
52
Units of labor employed, workers (L)
0
1
2
3
4
5
6
7
8
9
10
Explanation / Answer
Table 2. The production isoquant curve for Q = 29 tons Combination Labor Capital MRTS Total Cost (a) (b) (c) (d) (e) A 2 1500 400 B 2 1250 #DIV/0! 350 C 3 750 -500 300 D 4 500 -250 300 E 6 250 -125 350 MRTS = (change in capital)/(Change in Labor) Total cost = 50*L + 0.20*K
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